1. **State the problem:** Solve the equation $2800 + 38x = 3100$ for $x$. 2. **Isolate the term with $x$:** Subtract 2800 from both sides to get rid of the constant on the left. $$2800 + 38x - \cancel{2800} = 3100 - \cancel{2800}$$ This simplifies to: $$38x = 300$$ 3. **Solve for $x$:** Divide both sides by 38 to isolate $x$. $$\frac{38x}{\cancel{38}} = \frac{300}{\cancel{38}}$$ Which simplifies to: $$x = \frac{300}{38}$$ 4. **Calculate the value:** $$x \approx 7.8947$$ **Final answer:** $$x \approx 7.8947$$